Method of manufacturing a longitudinal mode mechanical vibrator



Aug. 5, 1958 v R. ADLER METHOD OF MANUFACTUR MODE MECHANIC ING ALONGITUDINAh. AL VIBRATOR Filed March 11, 1

INVENTOR. jEoerz c/Qaller 2% bornqg United Stats METHOD OF MANUFACTURINGA LON GITU- DINAL MODE MECHANICAL VIBRATOR Robert Adler, Nortlifield,Ill., assignor to Zenith Radio Corporation, a corporation of DelawareThe present invention relates to longitudinal mode mechanical resonatorsof the type used in ultrasonic generators and the like. Moreparticularly, it relates to a new and improved method for adjusting theresonant frequency of such resonators to an accurately predeterminedvalue.

As is generally known, a bar or rod formed from any of a wide variety ofmaterials such as metals, glass, ceramics, etc., can be made tomechanically vibrate in a longitudinal mode when shock-excited by asharp blow from a hammer moving along its longitudinal axis. Themechanical energy delivered to the resonator in this manner subsequentlymanifests itself as a mechanical vibration having an amplitude which isinitially at a peak and which decays exponentially with the passage oftime. Such vibration normally has a fundamental frequency componentwhich is determined primarily by the physical length of the resonatorand the propagation velocity of sound in the material from which theresonator is formed. Generally, the physical length of the resonatorrepresents a half-wave length at the fundamental frequency, hencemaximum particle displacement occurs at the extreme ends of theresonator while a vibration node appears at the exact physical center.In the region of this nodal plane there is no particle displacement butmerely a cyclic stressing of the material in tension and compresison.The amplitude of displacement of any particular particle occupying aposition intermediate the nodal plane and either end is a function ofthe physical distance between the transverse plane in which the particleresides and the nodal plane.

Mounting or supporting the resonator must be done in a particular mannerif excessive damping of the longitudinal vibrations by the supportmember is to be avoided. Since vibrational energy is primarilytransferred to the support member by the motion of the particles in theregion of contact between the support member and the resonator, it isdesirable that the support contact the resonator at a point of minimumparticle displacement. As has been previously stated, such a vibrationalnode exists throughout a transverse plane situated at the exact physicalcenter of the resonator. Contact between the support member and theresonator must be limited to this region if the damping effect of thesupport is to be minimized.

While there are many possible ways of mounting or supporting theresonator by mineral contact in this region, experience has shown that asupport of the type described and claimed in the copending applicationof Ole Wold, Serial No. 645,310, entitled Ultrasonic Generator, filedconcurrently herewith, now U. S. Patent 2,821,956 issued February 4,1958, and assigned to the same assignee as the present application,provides excellent positional stability with substantially negligibledamping. Such a support requires the removal of a small amountof'resonator material from the region of the nodal plane to form a pairof diametrically opposite relatively shallow transverse slots.

" atent O 2,845,591 Patented Aug. 5, 1958 To facilitate furtherexplanation, it may be helpful to consider the factors which affect thefundamental resonant frequency of the resonator. As has been stated, theresonant frequency is primarily determined by the physical length andthe propagation velocity of sound energy in the resonator. The latter isa function of the physical properties of the material from which theresonator is formed and hence is established and unalterable once aspecific material has been chosen. Accordingly, the desired resonantfrequency is normally arrived at by adjusting the physical length.Shortening the resonator decreases the period of vibration resulting inan equivalent increase in the resonant frequency. A third factor must beconsidered, however, if the mounting technique chosen requires theremoval of a portion of the resonator material in the region of thenodal plane. While such removal has no effect on the physical length ofthe resonator, it does reduce the stiffness of the resonator in thenodal region, and the reduced stiffness has been found to result in alowering of the fundamental frequency of vibration. This effect can beanalogized to a pair of equal masses interconnected with a spring havinga particular spring constant. If energy is imparted to the systemcausing the masses to oscillate in a direction parallel to thelongitudinal axis of the system, the frequency of oscillation will be afunction of the magnitude of the masses and the spring constant. Areduction in the stiffness of the spring results in a reduction in thespring constant and a lowering of the natural frequency of the system.While this efiect is less pronounced in the case of a resonator, sincethe stiffness is varied in but a relatively small portion of the system,the effect on the natural resonant frequency is qualitatively identical.

Should it be desired to mass produce, by conventional manufacturingtechniques, longitudinal-mode resonators of the type so far discussed,all of these factors become of increasing importance. Normally theapplication to which the resonators are to be put establishes thefrequency tolerance range within which all useful units so produced mustfall. In many applications, this range is sufficiently narrow to renderthe use of conventional mass-production techniques unsatisfactorywithout the introduction of an additional frequency adjustment procedureto reduce the frequency spread of the resultant resonators and to centerthis spread withinthe preestablished useful frequency range. It isnecessary that this frequency adjustment procedure be introducedsubsequent to the final step in the fabrication process if it is tocompensate for all tolerance effects which tend to introduce frequencyvariations. Additionally it is economically desirable that the procedurebe capable of supplying the prerequisite frequency accuracy without theuse of specialized high precision techniques or equip ment.

Accordingly, it is an object of the present invention to provide a newand improved method for adjusting the resonant frequency oflongitudinal-mode mechanical resonators of the type used in ultrasonicgenerators and the like.

It is a further object of the present invention to provide a new andimproved method for adjusting the resonant frequency of such resonatorsto an accurately predetermined value.

It is a still further object of the present invention to provide a newand improved method for adjusting the resonant frequency of suchresonators to an accurately predetermined value without the use ofprecision processing or special equipment.

In accordance with the method of the present invention, a longitudinalmode resonator or vibrator is first fabricated to such dimensions thatit exhibits an actual The features of the invention which are believedto be novel are set forth with particularity in the appended claims. Theorganization and manner of operation of the invention, together withfurther objects and advantages thereof, may best be understood byreference to the following description taken in conjunction with theaccompanying drawings, in which like reference numerals refer to likeelements in the several figures, and in which:

Figure l is an exploded view of a device constructed in accordance withthe present invention;

Figure 2 is a cross-sectional view taken through transverse section 22of Figure 1.

Figure 1 shows a partially exploded view of a longitudinal moderesonator and mounting bracket assembly. Resonator or vibrator is ofcircular cross-section and is shown longitudinally displaced from itsnormal operative position Within aperture 14 of bracket 11 to bettershow certain structural details.

Resonator 10 is preferably formed from aluminum or a similar metalhaving a low internal damping factor. A pair of shallow transverse slots12 are positioned at the exact physical center of the resonator, eachbeing diametrically opposite the other. A frequency adjustment hole of apredetermined depth is shown symmetrically disposed about the transversenodal plane which passes through the exact physical centers oftransverse slots 12. The factors which determine the depth-of hole 15are discussed in considerable detail later in this specification. Therelationships existing between slots 12 and hole 15 are more clearlyshown in the cross-sectional view of Figure 2.

Mounting bracket 11 contains a central aperture 14 of suflicientdiameter to permit the free passage ofresonator 10. A pair of resilientsupport members 13 formed from a single length of piano wire or the likeare positioned across aperture 14 and are supportably locked to bracket11 by slots 16 of appropriate contour.

Bracket 11 and resonator 10 are assembled by first outwardly deformingresilient support members 13 and then advancing resonator 10 throughaperture 14 .until support members 13 engage slots 12. The inwardlydirected forces exerted by support members 13 on resonator 10, whichresult from the outward deformation, serve to lock resonator 10 withinaperture 14, the contact between resonator 10 and support members 13being restricted to four'discrete points within transverse slots 12. Theadvantages and structural details of this mount are disclosed in theaforementioned copending application and hence further discussion isdeemed unnecessary.

Several factors should be kept in mind, however, to facilitate a betterunderstanding of the frequency adjustment method herein to be described.Conventionally, the desired resonant frequency of a resonator of thistype is established by adjusting the overall length of the resonatorsuch that it represents a half-wave length at the desired frequency ofvibration. The removal of the-necessary material to form transverseslots 12 has the effect .of lowering the resonant frequency below thatwhich would result on the basis of its length alone. As has been statedthis is a result of the reduction in the stiffnessof the resonator inthe nodal region. With these factors in mind, it is readily apparentthat some compensation must be made in the physical length of .theresonators 4 to offset the frequency lowering effect of the transverseslots, if the resonators are to exhibit final resonant, frequences whichfall within a relatively narrow predetermined range. When an attempt ismade to fabricate large numbers of such resonators by conventionalmassproduction machining techniques, the required compensationintroduces difficulties because of normal variations in the compositionof the raw stock from which the resonators are formed and the tolerancesassociated with the fabrication process. Experience has shown thatunless some means is provided for adjusting the resonant frequenciessubsequent to the completion of the forming process, rejection rates arehigh based on frequency deviations beyond the pre-established usefultolerance range.

For resonator applications which impose reasonably exacting frequencyrequirements, this difiiculty is avoided by fabricating and adjustingthe natural frequency of the resonators in accordance with the method ofthe present invention. The resonators are formed having a physicallength which is a predetermined amount shorter than that dictated by thedesired accurately predetermined frequency. The resulting resonatorsthence exhibit resonant frequencies which extend over a relatively widefinite range, the mean frequency of which is higher than the finaldesired frequency by a predetermined amount. The transverse mountingslots are then formed in any well known manner. This has thepreviously-mentioned effect of reducing the rigidity of the resonatorsin the nodal region, and a slight net reduction in resonantfrequencyresults. By properly choosing the length of the resonators, a criterionis established in which this net reduction in frequency is just adequateto shift the frequency range to a point in the frequency domain at whichthe'lower extremity of the range substantially coincides with the meanfrequency of the pre-established useful tolerance range, i. e., thedesired predetermined frequency. The resultant range of resonantfrequencies exhibited by the resonators in their completed form is thendivided into a plurality of adjacent zones each of a frequency widthslightly narrower than the width of the pre-established useful tolerancerange. The resonant frequency of each of the resonators is then checkedagainst a standard which exhibits a resonant frequency centered in theuseful tolerance range, to determine the amount by which the frequencyof each of the rsonators deviates from the standard and accordingly,into which of the discrete zones it falls. In this manner, a pluralityof discrete resonator groups are formed, there being the same number ofgroups as there are zones. All of the resonators falling into any givengroup are subjected to the same frequency adjustment comprising theremoval of material by drilling out a portion of the resonator withinthe region of the nodal plane; the depth of the hole, i. e., the amountof material removed, being approximately proportional to the frequencychange required to shift the mean frequency of the group to the point inthe frequency domain at which it coincides with the mean frequency ofthe pre-established useful tolerance range. All of the resonatorscontained within the group are shifted by like amounts, hence all residewithin the useful tolerance range by virtue of the fact that the widthof each of the groups was made slightly smaller than the width of theuseful range. Like adjustments are made on the resonators contained inthe remaining groups with the exception that differing amounts ofmaterial must be removed from the resonators in each group, the amountsbeing approximately proportional to the frequency difference whichexists between the mean frequency of the group and the mean frequency ofthe useful tolerance range.

While material may be removed from the nodal region of the resonators ina variety of ways, experience has shown that removal by drilling along atransverse axis substantially within the plane has advantages not foundin other techniques. A conventional drill press can be used with asimple V-block supplying the necessary support to the resonator duringthe drilling operation. Appropriately adjusted stops determine the depthof the hole and hence the amount of material removed. Each of a numberof drill presses corresponding to the number of groups can bepreadjusted to remove the correct amount of material from the resonatorscontained in a particular group, thus no skill is demanded of theoperator beyond that required to correlate a given resonator group withthe corresponding drill press. In this manner the desired frequencyadjustment is readily accomplished without the utilization of specialmachining techniques of a more expensive or time consuming nature.

In addition to these enumerated advantages, the fundamental concept offrequency adjustment by the removal of material from the region of thenodal plane eliminates a basic difficulty encountered in moreconventional techniques. As has already been established, it isessential that the support means contact the resonator in the region ofthe nodal plane if excessive damping is to be avoided. If the moreconventional frequency adjustment technique of varying the physicallength of the resonator is used, certain strict requirements must besatisfied if the result is to be satisfactory. Care must be exercised toinsure that equal amounts of material are removed from each end of theresonator if shifting of the nodal plane is to be avoided. Any unbalancein the quantities removed has the effect of shifting the nodal planeaway from the plane of the transverse mounting slots toward the side ofgreater mass. Such a displacement of the nodal plane places the mountingslots at a point where particle displacement occurs and vibrationalenergy is lost to the support with a corresponding reduction in theefliciency of the resonator. Accordingly, it is readily apparent thatsuch a method requires the use of machining techniques and skillconsiderably beyond that required by the method of the presentinvention. Additionally, the working of both faces of the resonatorstends to introduce additional frequency variations due to cumulativetolerance effects which are considerably more pronounced than thoseassociated with a relatively simple drilling operation.

Merely by way of illustration and in no sense by way of limitation thefollowing is given as an example of the frequency accuracy obtainable inthe mass production of 40 kc. longitudinal-mode mechanical resonators byfabrication and adjustment in accordance with the method of the presentinvention. The resonators were fabricated to a length such that anaverage resonator exhibited a frequency approximately 120 cycles persecond above the desired 40 kilocycles per second (kc.). The remainingsamples were found to occupy a range 250 cycles wide centered about40,120 cycles per second. This range was divided into five discreteadjacent zones of 50 cycles width and the resonators falling into eachof the resultant groups were frequency adjusted by drilling away anamount of material in the nodal region which was proportional to thefrequency difiierence which existed between the actual mean frequency ofthe group and the desired 40 kc. A standard number 56 drill was usedwhich resulted in drill stops approximately one sixteenth of an inchapart with the deepest hole passing almost through the resonators in thegroup requiring maximum frequency adjustment. Upon completion of theprocess, all of the samples were then found to fall in a tolerance rangeof 40 kc. plus or minus 30 cycles per second. This represents afrequency accuracy of better than plus or minus .08% obtained withconventional low precision machining techniques.

Accordingly, by utilizing the method of the present invention,longitudinal-mode mechanical resonators which have accuratelypredetermined resonant frequencies can be mass produced. The effects ofnormal manufacturing tolerances are readily compensated by a finalfrequency adjustment which is accomplished in a manner which eliminatesthe need for precision processing and hence permits the use ofconventional machining techniques. Experience has shown that resonatorsfabricated and frequency adjusted by this method fall within theallowable frequency tolerance range with such a regularity that no finalfrequency check is required before they are installed in the apparatusfor which they are intended.

Resonators produced by the method of the present invention are useful inultrasonic apparatus of the type fully described and claimed in thecopending application of Robert Adler, Serial No. 578,333, filed April16, 1956, now U. S. Patent 2,821,954 issued February 4, 1958 anddivisional U. S. Patent 2,817,025 issued December 17, 1957 and entitledControl System, respectively, and that of Robert Ehlers and Clarence W.Wandrey, Serial No. 645,091 entitled Ultrasonic Transmitter and, filedconcurrently herewith, now U. S. Patent 2,821,955 issued February 4,1958, all of which are assigned to the same assignee as the presentapplication.

While a particular embodiment of the present invention has been shownand described, it is apparent that changes and modifications may be madewithout departing from the invention in its broader aspects. The aim ofthe appended claims, therefore, is to cover all such changes andmodifications as fall within the true spirit and scope of the invention.

I claim:

1. The method of manufacturing a longitudinal-mode mechanical vibratorhaving an accurately predetermined resonant fundamental frequency whichcomprises: fabricating an elongated vibrator element having an actuallongitudinal-mode resonant fundamental frequency slightly higher thansaid predetermined fundamental frequency; and removing material from anintermediate portion of said element coincident with and substantiallywithin a nodal plane for vibrations at said fundamental frequency in anamount substantially proportional to the difference between said actualand predetermined fundamental frequencies to reduce its resonantfundamental frequency from said actual fundamental frequency to saidpredetermined fundamental frequency.

2. The method of manufacturing a longitudinal-mode mechanical vibratorhaving an accurately predetermined resonant fundamental frequency whichcomprises: fabricating an elongated vibrator element having an actuallongitudinal-mode resonant fundamental frequency slightly higher thansaid predetermined fundamental frequency; and drilling away materialfrom an intermediate portion of said element coincident with andsubstantially within a nodal plane for vibrations at said fundamentalfrequency in an amount substantially proportional to the differencebetween said actual and predetermined fundamental frequencies to reduceits resonant frequency from said actual fundamental frequency to saidpredetermined fundamental frequency.

3. The method of manufacturing a longitudinal-mode mechanical vibratorhaving an accurately predetermined resonant fundamental frequency whichcomprises: fabricating a cylindrical rod having a length slightlyshorter than one-half wave length in said rod at said predeterminedresonant fundamental frequency and adapted for longitudinal-modevibrations at an actual fundamental frequency slightly higher than saidpredetermined fundamental frequency when supported at its central nodalplane for vibrations at said fundamental frequency; and drilling awaymaterial from said rod substantially within said central nodal plane inan amount substantially proportional to the difference between saidactual and said predetermined fundamental frequencies to reduce its resonant fundamental frequency to said predetermined fundamental frequency.

4. The method of manufacturing a longitudinal-mode mechanical vibratorhaving an accurately predetermined resonant fundamental frequency whichcomprises: fabricating an elongated vibrator element having a length 7 8slightly shorter. than one-half wavelength in said element ReferencesCited in the file of this patent at said predetermined fundamentalfrequency; testing said UNITED STATES PATENTS element to determine itsactual longitudinal-mode reso- V r t nant fundamental frequency; andremoving material from 2,655,069 m 3 an intermediate portion of saidelement coincidentwith 5 2 3 Y M 5' andv substantially within a nodalplane for vibrations at 2,728,902 Whne 1955 said fundamental frequencyin an amount substantially I I proportional to the difierence betweensaid actual and REFERENCES I v predetermined fundamental frequencies toreduce its funbQ k Sound, wood, G; 13911 & 0 damental frequency fromsaid actual fundamental fre- 10 London, 1946, Fagcs 111-121 and 140444felled quency to said predetermined fundamental frequency.

